, Volume 49, Issue 2, pp 187-190

The existence of maximal slicings in asymptotically flat spacetimes

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Abstract

We consider Cauchy data (g, π) on IR3 that are asymptotically Euclidean and that satisfy the vacuum constraint equations of general relativity. Only those (g, π) are treated that can be joined by a curve of “sufficiently bounded” initial data to the trivial data (δ, 0). It is shown that in the Cauchy developments of such data, the maximal slicing condition tr π=0 can always be satisfied. The proof uses the recently introduced “weighted Sobolev spaces” of Nirenberg, Walker, and Cantor.

Research partially supported by National Science Foundation Grants GP-39060 and GP-15735
Research partially supported by National Science Foundation Grant GP-43909 to the University of North Carolina
Communicated by J. Ehlers